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Limits and Derivatives

JEE Main 2024 (Online) 29th January Morning ShiftMCQMedium📈 Topic in 33% papers+4−1
Ques. 1JEE Main 2024, 29 January (Morning Shift)

x 2 ( 1 (x- 2 )2 x3 ( 2 )3 (t 13 )dt ) is equal to

  1. 3 24
  2. 3 28
  3. 3 4
  4. 3 8

Answer

(2) 3 28

Solution

Form 00 ⇒ L'Hôpital's rule, with Leibnitz rule: ddx x3( /2)3 (t 13 )dt=- x 3x2

L= x 2 -3x2 x2 (x- 2 )

∵ x=- (x- 2 )

L= x 2 3x22 (x- 2 )x- 2= 32 24 1= 3 28

Answer: (2)

Keep practising — Limits and Derivatives

Ques. 2JEE Main 2024, 29 January (Evening Shift)

Let the slope of the line 45x+5y+3=0 be 27r1+ 9r22 for some r1, r2 R. Then x 3 ( 3x 8t2 3r2x2-r2x2-r1x3-3x dt ) is equal to .

Ques. 3JEE Main 2024, 27 January (Morning Shift)

If a= x 0 1+ 1+x4- 2x4 and b= x 0 2x 2- 1+ x, then the value of ab3 is :

  1. 36
  2. 25
  3. 32
  4. 30
Ques. 4JEE Main 2024, 27 January (Evening Shift)

If x 0 3+ x+ x+ e(1-x)3 2x= 13, then 2 - is equal to :

  1. 2
  2. 1
  3. 5
  4. 7

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